What does the narrator think about the owner of the woods?

The speaker of Frost's poem knows to whom the woods belong.

While at first he does not seem worried about trespassing because the owner will not see him,

Whose woods these are I think I know....   He will not see me stopping here   To watch his woods fill up with snow.

there is yet the sense that the speaker feels he is committing some sort of violation as he remarks that his horse...

The speaker of Frost's poem knows to whom the woods belong.

While at first he does not seem worried about trespassing because the owner will not see him,

Whose woods these are I think I know....   
He will not see me stopping here   
To watch his woods fill up with snow.

there is yet the sense that the speaker feels he is committing some sort of violation as he remarks that his horse must think it odd that they have stopped because there is no farmhouse or barn nearby: 

He gives his harness bells a shake   

To ask if there is some mistake.

In addition, there is a sense of hesitation and doubt generated by the phrase of the first line: "I think I know." The horse is stopped, and he shakes his head; then, although the speaker professes that he has a long way to go, he remains in the spot at which he has stopped. This static quality is emphasized by the rhyme scheme of the poem: aaba bbcb cede. For the second stanza picks up the rhyme of line b in the first, and the third stanza carries along line c, thus generating little movement.